geoscientists guide to petrophysics
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Foreword
As its name implies, petrophysics is the study and measurement of the physical properties of
rocks. As soon as you start to take an interest in this field, you are struck by the duality
between the Physics aspects and the Geology aspects. In most publications, the
Physics aspect prevails, in other words the quantitative description of the laws governing
the phenomena affecting the rocks subject to various stresses: hydraulic, mechanical,
electrical, etc. The rock itself is generally no more than a black box whose microscopic
structure is never described, or at best very briefly, as a model sometimes far remote from
reality. This is because the evident rich diversity of the natural porous media scares the
physicist, as expressed so well by G. Matheron [in French, 1967] ces millions de grains
et la varit inpuisable de leurs formes et de leurs dimensions.
(these millions of
grains and the inexhaustible variety in their shapes and dimensions.
Yet, how can we understand the anomalies sometimes observed in fluid flow or capillary
equilibria within a rock without a vital piece of information, the description of a feature in
the geometry of the pore space? But above all, if we are to scale up highly isolated
petrophysical observations to an entire oil reservoir or an aquifer, it is essential to implement
the powerful extrapolation tool of geological interpretation. This is clearly based on a
good understanding of the relations between the petrophysical parameters studied and thepetrological characteristics of the rock considered. This Geological approach of
Petrophysics is at the hub of our project.
Firstly, however, we must define our perception of the field of petrophysics and clarify
the terminology, since two virtually identical terms, Rock Physics and Petrophysics
coexist.
The term Rock Physics was popularised by Amos Nur, who developed a famous
Rock Physics laboratory at Stanford University in the 70s. The field assigned to Rock
Physics is basically both quite simple to define and extremely vast: study the physical
properties of geological materials, focusing in particular on the properties implemented in
the various applications: electrical, hydraulic, nuclear, mechanical (static and dynamic)
properties. The term Petrophysics, which is older (G. Archie?), initially referred to the
study of reservoir properties in an exclusively petroleum environment. At the presenttime, both terms coexist and are used in slightly different ways (although the distinction
remains vague): Rock Physics is used mainly in university environments, often
concerning mechanical or magnetic properties; Petrophysics is preferred by the oil
exploration-production community, with a strong emphasis on hydraulics. A quick search
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VIII
Foreword
for these two key words on an Internet search engine gives approximately the same number
of hits for Petrophysics and Rock Physics.A relatively recent terminological evolution is noticeable, resulting in the inclusion of
Log Analysis in Petrophysics. In 2000, the journal The Log Analyst published by the
Society of Petrophysicists and Well Log Analysts (SPWLA), was renamed Petrophysics.
In this book we will only use the term Petrophysics and consider it in its usual
common meaning, which is slightly restrictive: study of the physical properties of rocks
focusing on the storage and flow of the fluids contained within them. We will investigate
more specifically the properties related to the greater or lesser presence of a porous phase
inside the rocks. This porosity will play a central role in our descriptions. The raison dtre
of Petrophysics, as we will describe it, lies mainly in its relation to petroleum,
hydrogeological and civil engineering applications.
The book is divided into two sections of unequal size:
The first section (by far the largest in terms of the number of pages) describes the
various petrophysical properties of rocks
. Each property is defined, limiting the
mathematical formulation to the strict minimum but emphasising, using very simple models,
the geometrical (and therefore petrological) parameters governing this property
. The
description of the measurement methods is restricted to an overview of the principles
required for good communication between the geoscientist and the laboratory
petrophysicist. For each property, we detail one or two aspects of the relations between
petrophysics and geology which we feel are of special interest (e.g. the porosity/
permeability relations in carbonate rocks for single-phase permeability, or irregular water
tables and stratigraphic traps for capillary equilibria).
The various properties are classified into three subsets according to their main use in the
study of oil reservoirs or aquifers (this organisation also allows us to consider the cases of
perfect wettability and intermediate wettability separately, making it easier to exposecapillary phenomena):
a) Calculation of fluid volumes (accumulations)
; Static properties: Porosity
and
C
apillary Pressure
in case of perfect wettability.
b) Fluid recuperation and modelling;
Dynamic properties:
Intrinsic permeability
,
Wettability
,Relative Permeability
and End Points.
c) Log and geophysical analysis;Electrical properties
: Formation factor and saturation
exponent,Acoustic properties:
Elastic wave velocity,Nuclear Magnetic Resonance
and its
petrophysical applications. This third subset acts as a link with log analysis, a technique
which is increasingly considered as being part of petrophysics. We provide a description of
the most general principles without discussing log analysis as such.
The second section,
which concentrates on methodological problems, provides a few
notions which are at the root of the problems on the understanding and applicability ofpetrophysics.
It concerns, above all, the representativeness of the measurements and the size
effects, so important for extrapolation of results and characterisation of reservoirs.
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Foreword
IX
In this context we describe a few general points on the
effect of stresses and temperature
on the petrophysical characteristics. These effects are described separately for each property,however, in the first section. We therefore decided, perhaps rather over-simplifying matters
in the process, to consider compressibility as the effect of stresses on the porosity.
The notions ofRepresentative Elementary Volume, Homogeneity, Anisotropy
provide a
better understanding of the problems of up-scaling
, for which a few examples are given
(plug, core, log analysis, well test). After giving the most pragmatic definitions possible, we
give a few examples concerningpermeability anisotropy
or the consequences of
saturation
inhomogeneity
on the acoustic or electrical properties. The consequences of these size
effects in reservoir geology are particularly spectacular in the contrast between matrix
property (centimetric scale) and bulk properties (plurimetric scale) as observed in the
fractured reservoirs, which will only be discussed briefly.
We then mention the extrapolation of petrophysical properties and characterisation of
reservoirs using theRock Typing methods
which still remain to be defined, a clear consensusnot having yet been reached.
Lastly, we provide a description of several Porous Network investigation methods
.
We
describe in short chapters the methods used to observe these networks at various scales: Thin
sections, Pore Casts, Visualization of capillary properties, X-ray tomography
. Each method
offers an opportunity to give a few examples of porous geometries. A brief overview of
X-ray diffraction
technique is proposed.
Concerning the
Bibliography
, we decided not to follow a certain inflationist trend. We
restricted the list to the English texts explicitly referred to in the document. We made
occasional exceptions to this language rule for some reference documents or for French
documents from which we have extracted data.
We wanted to pay special attention to the Index
, mainly since we know from experience
just how important this is for readers. But also since a detailed index simplifies the plan.Rather than trying to produce a perfect logical order to introduce various notions, which
rapidly turns out to be a very difficult task, we decided instead to insert numerous cross-
references in the text, allowing readers to obtain all the details they need. The numerous
porosity terms are often confusing, we try to clarify this in a
porosity terms glossary-
index
.
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62 Chapter 1-1 Calculation of Fluid Volumes In Situ (Accumulations): Static Properties
Figure 1-1.32 Example showing the location of the non-wetting fraction trappedby imbibition in natural porous media
Photograph of thin sections prepared according to the resin spontaneous imbibition method (see 2-2.2.2).
The red resin corresponds to the fraction of non-wetting fluid displaceable by spontaneous imbibition. The
yellow resin corresponds to the fraction trapped during imbibition.
a) Bioclastic grainstone; b) large bioclast in an oolitic grainstone; c) and d) vuggy dolomite. Notice the role
of residual crystallisation (c) in limiting the capillary trapping.
The photographs on Figure2-2.13, correspond to the same visualization method.
2 mm
1 mm
Trapped non-wetting phase
Displaceable non-wetting phase
(Spontaneous imbition)b
c d
a
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66 Chapter 1-1 Calculation of Fluid Volumes In Situ (Accumulations): Static Properties
A) Soil specificity
a) Specificity concerning the physical processes
Regarding the physical process, soil specificity is fundamental since the total volume of a
soil sample may vary depending on the water content. This is not the case for reservoir
rocks, which contain water and/or hydrocarbons and whose total volume (anda fortiorithe
volume of the solid phase) is considered as invariant: any loss of liquid in terms of volume
leads to desaturation, and vice versa.
In a soil, loss of water first results in a reduction in total volume, the saturation index
remaining equal to100%. Then, beyond a water content limit known as the shrinkage
limit, the soil behaves as a rigid rock and loss of water leads to desaturation of the porous
space (see Fig. 1-1.5, p. 15).
In practice therefore, the water volume is either compared with the solid volume or to the
dry mass in order to obtain an invariant. This leads to an abundance of definitions,sometimes a source of confusion, which will be summarised below, using the volume and
mass parameters described in 1-1.1.2 (p. 5): VV,VS, VT, VWrespectively the void, solid
and total volumes (Vt = Vv + Vs) and the water volume contained in the porous medium;WSthe dry mass and WWthe water mass:
Porosity: = VV/VTThe letter n is used in soil physics and soil mechanics (and
sometimes f in hydrogeology, instead of ).
Void ratio: E= VV/VSwhere E= /(1 ), often written e.
Saturation index SW= VW/VV(saturation in petroleum terminology). In soil phys-
ics and soil mechanics, SRis often used instead of SW.
Soil moisture: W = WW/WS. The term water content is frequently employedinstead of soil moisture and written w or
Volume water content: V= WW/VTThis term is often confused with the expressionVW/VTsince these notions are used in soil mechanics and in soil physics where the
assumption is made that w= 1000 kg/m3(freshwater).
b) Specificity concerning the methodological approach
There are a certain number of specificities in the study of soil capillarity which correspond
to methodological differences:
In petroleum petrophysics, due to the specialisation of the technical teams, petrophysi-
cists mostly disregard fluid movement related to capillary forces. These studies belong
to the field of reservoir modelling. Consequently, it is the capillary pressure curve as
such which is studied. In soil sciences however, this specialisation is less obvious and
the movement of fluids (water in fact) is an integral part of the studies on capillarity.
This leads to the definition of potentials (moisture, gravity, etc.). Since our objective isprimarily to highlight the similarities between petroleum methods and soil sciences,
independently of terminology differences, we will first describe the equivalent of the
capillary pressure curve. We will then briefly discuss the movements of water in soil.
One of the main applications of soil science is agronomy. It is not surprising that
plants (especially their roots) play a major role, extending as far as the definition of
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1-1.2 Capillary Pressure in Case of Perfect Wettability 67
capillary properties. The maximum capillary pressure that can be overcome by the
roots to extract water from the soil is one of the major parameters of the capillarypressure curve (wilting point).
B) Curve of capillary pressure in soils
a) Matrix potential curve
Figure 1-1.35, found in various forms in hydrogeology or pedology books [e.g. de Marsily,
1986] is the equivalent of the capillary pressure curve described in the previous paragraphs.
The terminology differences must nevertheless be taken into account.
The y-axis does not strictly correspond to a pressure (Pc) but to a moisture potential
(m), (also called suction matrix potential, matrix potential or capillary potential. It
corresponds to the energy required to extract a unit mass of water fixed by the capillary
forces. Note that:
this physical quantity is expressed in practice as equivalent water height. We thereforeobtain the same hydrostatic formula Pc = h as that used in 1-1.2.6 (p. 102) to
explain the saturation profiles in hydrocarbon reservoirs;
in soil science applications, the air is virtually always at atmospheric pressure, which
is taken as zero for pressure difference measurements. Since the capillary pressure is
equal to the pressure difference between the non-wetting fluid (air, reference pressure
Figure 1-1.35 Curve of suction matrix potential against water content(equivalent, in soil science, of the capillary pressure curve)
Soil moisture
Saturation
Intermediaire
cycleDrying
Moistening
W
Matrixpotential(suction
)
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68 Chapter 1-1 Calculation of Fluid Volumes In Situ (Accumulations): Static Properties
zero) and the wetting fluid -water), the pressures in water are negative. This explains
why we speak of suction; For historical reasons (in reference to the former CGS system of units), these heights
are converted into centimetres. Since the range encountered extends over several
orders of magnitude, the heights are expressed in logarithmic form. The moisture
potential pF is therefore equal to the decimal logarithm of the capillary suction
expressed in centimetres of water, taking into account the sign inversion inherent to
the use of the term suction.
Other sources of terminology confusion are given below: In the field of petroleum, and
in the case of water-wet media, we have defined the two hysteresis branches:
drainage: branch describing the decrease in water saturation;
imbibition: branch describing the increase in water saturation;
In soil science, the term drainage is reserved for the water evacuation process
during consolidation (water-saturated soils). the branch describing the decrease in water saturation is often called drying;
the branch describing the increase in water saturation is called humidification, mois-
tening or rewetting.
b) Order of magnitude of moisture potentials
We have defined the potential pF as the decimal logarithm of the capillary suction
expressed in centimetres of water. The orders of magnitude observed in soils are listed in
Table 1-1.8. Note that the range of values is much broader than that generally considered for
reservoir rocks.
c) Specific retention, Wilting point
By convention, pedologists identify two singular points on the pF curve:
A point corresponding to pF = 2 (100 cm of water) corresponding to the specific
retention of the soil expressed in volume content, equivalent to the hydrogeological
notion of field capacity (weight content): if the pF is less, the soil is assumed to dry
spontaneously (i.e. allow the water to flow by gravity).
A wilting point corresponding to the energy beyond which plants cannot extract water
from the soil, and set by convention at pF = 4.2 (16 000 cm of water, i.e. 1.57 MPa).
d) Soil water reserve
The difference between the volume water content at pF = 2 (specific retention or field
capacity) and the volume water content at pF = 4.2 (wilting point) defines the soil
Available Storage (AS) (or available reserve). The Field capacity is also called the
Water Storage Capacity (WSC). We sometimes even speak of an Available Moisture
(AM) limited by the water content to pF = 3. Some authors define it even more empirically:
1/3 or 2/3 of the AS, or 1/3 of the Water Storage Capacity (WSC).
These characteristics are schematised on Figure 1-1.36. We observe a certain similarity
with the distinctions made by petroleum petrophysicists (Fig. 1-1.10, p. 20). The most
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1-1.2 Capillary Pressure in Case of Perfect Wettability 69
interesting similarity is that between the notion of wilting point used in soil physics and
that of irreducible water saturation used in petroleum petrophysics. This similarity will
also apply below, when we examine polyphase flows.
In these notions of soil water reserves, we find ambiguities similar to those observed in
the definition of petroleum reserves. Initially, these concepts were determined to quantify
the water available in the soil for vegetation. The capacity of plants to extract water
obviously varies from one species to another. In addition, the limit defining the field
capacity is purely empirical. Determination of AS or AM based on a range of pF
values is therefore conventional and corresponds to a usual value, obtained by observation
and experiment and mainly involving crops.
We must also mention two other sources of ambiguity:
Soil physicists working in the field of pedology generally express volumes in water
height by analogy with pluviometries and in order to make comparisons. The diffi-
culty arises not so much in the conversion of volume into height per unit area, but in
the determination of the depth of soil concerned. Strictly speaking, it can only be the
Table 1-1.8 Order of magnitude of moisture potentials pF and pore throat equivalent radii(data from Baize [2004, in French] and Banton and Bangoy [1999, in French]
Suction
(Equivalent negative
pressure)
Hydraulic headPore throat
equivalent
radius
Remarks
kPa
(102 Bar)atm
Water
column
(cm)
pF
0.1 0.001 1 0 1.5 mmPedologists macroporosity
1 0.01 10.2 1.1 0.15 mm
10 0.1 102 2 0.015 mm Specific retention
98 0.967 1 000 3 1.5 mLimit of classical tensiometers
in situ
1 000 10 10 200 4.0 0.15 m
In situmeasurements:
limit of new-generation
tensiometers
start of the field of
psychrometric measurements
1 569 15.48 16 000 4.2 0.094 m Wilting point
7 000 69 71 400 4.85 0.021 m
Limit of psychrometric
measurements in situ
(95% humidity)
9 804 100 100 000 5 0.015 mAir-dried soil
(relative moisture 92%)
98 039 1 000 1 000 000 6 0.0015 mAir-dried soil
(relative moisture 48%)
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70 Chapter 1-1 Calculation of Fluid Volumes In Situ (Accumulations): Static Properties
depth reached by the roots of the plants (cereals, trees, etc.) concerned and not the
total thickness of the pedological soil or the geological surface formation considered.
This leads to the other conceptual difficulty: a difference must be made between the
potential total volume of a pedological horizon and the water actually available at a
given time. This explains why modern agronomist make a clear distinction between
the notion ofstorage and the notion ofreserve .
It is interesting to point out the analogy with a notion also sometimes unclear in oil
exploration, but which the petroleum engineers have had to strictly define by rigorously
identifying the notion of hydrocarbon accumulation and the notion of reserves.
C) Total soil water potential and water movement in soils
The study of water movements in soils is clearly fundamental for soil science specialists and
hydrogeologists. However, petrographers studying diagenesis (cementation, compaction) of
sediments in the vadose zone, i.e. the zone very close to the surface in two-phase water/air
saturation, also require a knowledge of these movements. Vadose diagenesis is of
paramount importance in the study of numerous carbonate rocks, for example.
The generalised notion of total soil water potential is used to describe these movements.
It is a physical quantity expressing the potential energy of water per unit mass, volume or
weight of soil considered. Its dimensions vary depending on the definition used.
We will continue using the unit equivalent water height, as we did for capillary pressures.
Figure 1-1.36 Occupation of soil porosity by water. Diagrammatic representation of various types of reserve
Intrinsic characteristics
Free water
Specific retention
Capillary water
absorbable by roots
Capillary water
not absorbable
Wilting point
Air
At time t.
Capilarywater
Totalporosity
WSC
AS
AM
R
W
2
4.2
3
PF
AS R
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1-1.2 Capillary Pressure in Case of Perfect Wettability 71
The potential () is divided into three main potentials:
= z+ m+ o
where:z= gravity potential
m= moisture potential (or capillary potential, matrix potential) described above
o= osmotic potential
The osmotic potential is induced by the difference in salt concentration across a
membrane, whether biological (plants) or mineral (clay).
Strictly speaking, an external potential (related to atmospheric pressure) and a kinetic
energy term related to the fluid speed should be added to the previous potential energies.
Since the flow speeds in porous media are generally very slow, however, this term is
negligible.
Note that mchanges sign and becomes a pressure potential (p) under the level of the
aquifer piezometric surface.The notion of total soil water potential is a very useful concept, since it provides an
overall picture of the system, considering the soil-plant-atmosphere continuum as a single
entity.
The possible water movements in the soil can therefore be identified. At a given time, the
water profile of a soil is imposed by the equilibrium between the influxes (precipitation)/
outfluxes (evaporation) on the soil surface and the capillary supply by the water table (in the
broad sense).
The flux direction will be determined by the potential difference between the two points
considered, from the higher to the lower. If, to a first order, the kinetic energy is neglected,
considering that the displacements are very slow, the total soil water potential is that defined
above: = z+ m+ o. In addition, the soil surface is usually taken as height reference.
Figure 1-1.37 gives a very simple and highly schematic example of the distribution ofthe these potentials and therefore of the possible water movement, taking into account only
the resultant of the moisture potential and the gravity potential. This problem is addressed
implicitly when describing capillary drainage ( 1-1.2.4B, p. 74) and more indirectly when
examining the distribution of fluids in hydrocarbon reservoirs (1-1.2.6, p. 102). In both
situations, however, we are dealing with equilibrium profiles, which is not the case here.
We will first consider the examples of saturation profiles (Fig. 1-1.37 a). From an
equilibrium profile (1) corresponding to the gravitational equilibrium of 1-1.2.4B, near the
soil surface, we observe variations due to the water influxes by precipitation (2) or water
outfluxes due to evaporation (3).
These saturation variations induce correlative variations in moisture potential
(Fig. 1-1.37 b). Since we chose the water equivalent height as unit of potential, the capillary
equilibrium potential corresponds (by definition) to a straight line of gradient 1 cutting they-axis at a negative value equal to the depth of the free (piezometric) water table. The influx
or outflux profiles correspond to curves tending towards lower values for the outfluxes and
higher values for the influxes (obviously, these are not absolute values but negative
algebraic values).
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72 Chapter 1-1 Calculation of Fluid Volumes In Situ (Accumulations): Static Properties
The gravity potential corresponds to a straight line of gradient 1 going through the origin
of the graph (soil surface).
In the simple hypothesis chosen, the water potential is equal to the sum of the previous
ones. The resulting profile (Fig. 1-1.37 c) corresponds to a vertical line (equipotential) for
the case of capillary equilibrium (by definition). In our examples of water influx and
outflux, the potentials are locally greater or less than this equipotential, the water fluxes
occurring either towards the top or the bottom.
Obviously, however, some saturation profiles may correspond to influxes and outfluxes
successively on the same vertical. The resulting potential will be more complicated
Figure 1-1.37 Highly diagrammatic example of distributions of potentials and saturations in a soil
a) Saturation profile and capillary pressure for a gravitational equilibrium state (1); water influx (2) or water
outflux (3).
b) Potential corresponding to these states.
c) resulting total potential.
d) Example of zone with influx and outflux resulting in a zero flux plane.
Total soil water potentialTotal soil water potential
Zero flux
plane
FluxFlux
He
ight
He
ight
00
0
0 1
He
ight
3 21
321
3 21
Free water table
Water saturation
Water potential
mcapillarypotential
ggravity
potentia
l
100%
capillary fringe
a)b)
c) d)
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90 Chapter 1-1 Calculation of Fluid Volumes In Situ (Accumulations): Static Properties
Figure 1-1.46 Continued, plate 2
0
0.03
0.010.11101001 00010 000
0.06
0.09
0.12
0.15
0.18
0.21
0.24
0.27
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Macroporosity
Microporosity
SCE
SCE
Shaly Sandstone
= 0.29
K = 86 mD B2
Pore filling
autigenic kaolinite
Grain coating illite
and illite/smectite
Pyrite
0.001
0.01
0.1
1
10
100
1 000
Frequency
P C
(Mpa)
SHg Equivalent access radius (m)
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1-1.2 Capillary Pressure in Case of Perfect Wettability 103
Hydrocarbons are driven to move by their buoyancy which is related to the difference
in density () between hydrocarbons (o, g) and water (w). This force is used toovercome the capillary barrier (capillary pressure) opposing the penetration of non-wetting
fluid. At the top of a hydrocarbon column of height h, the buoyancy induces a pressure
difference with respect to water (P = Po Pw) which is easy to calculate using the fluid
equilibrium formula: P = . .h, whereis the gravitational acceleration (see paragraph
B. a below for further details).
Movement of the hydrocarbons therefore implies coalescence into accumulations whose
height is sufficient to overcome the capillarity (see below B. a for orders of magnitude).
These accumulations will move upwards along the upper limits of the layers, or more precisely
the permeability-capillarity contrasts. These contrasts may represent relative barriers which
will be crossed when the height of the oil column has increased due to influx of additional
hydrocarbons. These contrasts may also correspond to absolute barriers if the permeabilities
are extremely low (compacted shale). This is the case of cap rocks which may lead to the
formation of a reservoir if the geometry of the impermeable rock allows a trap to develop.
If the geometric structure forms a trap, the hydrocarbons accumulate (from the top
towards the bottom of the trap). If the hydrocarbon influx is sufficient the geometric spill
point (Fig.1-150a), corresponding to the lowest point of the trap, may be reached. The
reservoir is full; the distance between the highest point of the trap and this spill point is
called the trap closure.
b) Capillary trapping (residual saturation) and traces of secondary migration
The notion of residual saturation caused by capillary trapping of a fraction of non-wetting
fluid is defined in 1-1.2.2.D, p. 59. At the end of the secondary migration, when there is no
further influx of hydrocarbons, this residual saturation should last in the transfer zones,
showing the path of the secondary migration.
Over the course of geological time, one might expect that the progressive disappearance
of residual fluids, especially gases, is due to solubilisation (if there is water movement in the
layer) or diffusion phenomena. As regards oil, an evolution into bituminous formations (tar-
mats) is more likely.
What is the true situation? It is extremely difficult to provide an objective answer. It
seems almost impossible to detect such traces of residual hydrocarbons, in fact, since they
would be limited to relatively thin layers of rock in contact with permeability contrasts.
Located by definition outside reservoirs, there is very little chance of samples being taken
from this type of zone during coring. In addition, it is very difficult to detect by log analysis.
We therefore see how difficult it is to provide an answer.
The notion of residual hydrocarbon also arises when, under the effect of tectonic
movements (e.g. tilting), the reservoir closure decreases (relative elevation of the spill point)and the trap partly empties. In this case, any residual traces are easier to locate. It is likely,
however, that there is a link between this residual fraction and the tar-mats sometimes
present in large quantities below the current oil/water contacts. It is also highly probable that
this phenomenon contributes to the uncertainty regarding the exact location of the oil/water
contact surfaces often observed in practice.
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106 Chapter 1-1 Calculation of Fluid Volumes In Situ (Accumulations): Static Properties
problem arising with this zone is how to determine the value of Swi, a matter of great
concern for reservoir specialists. We will discuss this subject briefly in 1-2.3.3,p. 186.
The transition zone where the two phases are movable (relative water and oil permea-
bilities non zero). The bottom of this zone corresponds to the appearance of hydrocar-
bons in the reservoir. This is the original (before start of production) oil-water contact
(OOWC) or gas-water contact (OGWC) which could be quite different from the free
water level (FWL).
The capillary foot (or capillary drag). This is a very special zone, totally water satu-
rated, but in which the (virtual) capillary pressure is non zero. The pore throat radius
is too narrow for the non-wetting fluid to enter. In practical reservoir geology applica-
tions, this zone is of considerable interest to provide an insight into original oil/water
contact (OOWC) anomalies.
c) Some simple examples of numerical values
We saw in 1-1.2.5 that we can estimate the scale conversion factor to graduate the
capillary pressure axis in heights above FWL, to obtain the diagram of a saturated reservoir.
To simplify matters, we will use mercury porosimetry curves as capillary pressure value
(ts= 460 mN/m, = 140). Although this may not be the best way to investigate the notion
of Swi, it is sufficient for our purposes, where the main objective is to examine the capillary
feet and the original oil/water contacts (OOWC). We will study a standard water/oil
(ts= 30 mN/m, = 0, = 200 kg/m3) and water/gas (ts= 50 mN/m, = 0, = 700 kg/m
3)
case (seeTable 1-1.7, p. 55).
On Figure 1-1.51, the maximum height scale (500 m) corresponds to the major
petroleum zones (remember that the height of the hydrocarbon column may exceed one
kilometre in some fields (e.g. the Middle East)).
At this scale, we mainly observe that:
The water/hydrocarbon contacts (OWC, GWC) correspond to the free water level
(y = 0 on Figure 1-1.51) for all the permeable reservoirs (single-phase permeability
greater than several tens of millidarcy). There is no difference between OOWC and
FWL when we consider the traditional sandstone reservoirs or the permeable carbon-
ate reservoirs. This explains the sometimes marked lack of interest for this problem.
In contrast, the capillary foot zone may take on considerable importance when deal-
ing with very low permeability reservoirs, especially micrite type limestone reservoirs
but also poorly porous sandstone reservoirs.
Obviously, due to the larger density difference, the problems of FWL/GWC shift are
less significant in gas reservoirs.
As soon as we start to move up in the structure, the water saturation gradient as a
function of the height is low, even with the simple calculation mode used (directlyrelated to the porosimetry access radii).
We must remember that these remarks apply to a high oil column (important
structuration and abundance of hydrocarbons). For poor petroleum provinces, the
problems may be quite different, for example for stratigraphic traps (see C. a and b below).
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1-1.2 Capillary Pressure in Case of Perfect Wettability 107
C) Applications to some practical aspects of reservoir geology
The above description of fluid distribution corresponds to the idealised case of a perfectly
homogeneous reservoir, both in terms of the petrophysical properties of the rock and those
of the saturating fluids. In nature, the situation is never that simple. The first cause of
complexity is due to the fact that natural reservoirs are heterogeneous. In this paragraph, we
will discuss a few cases of reservoir geology where the application of these simple capillary
equilibrium notions helps us to understand the phenomena involved.
a) Water/oil contact fluctuations
Determination of the water/oil contact and the free water level
As soon as we move away from the case of permeable reservoirs with zero transition zone,
determining the exact value of these two levels may be less trivial than it would first appear.
Determining the original oil/water contact corresponds to the appearance of the first oil
indices, which are not always easy to detect using log analysis in cases of low porosity and
saturation. There are two ways to determine the free water level: either by identifying the
oil/water contact in a drain with zero capillarity (in practice, an observation well left idle for
Figure 1-1.51 Examples of saturation profiles
500Clean sandstone, 0.24, 460 mD Bioclastic limestone, 0.28, 300 mD Micrite, 0.14
Heightabovefreewaterlevel(m)
400
300
200
100
0500
Shaly sandstone, 0.23, 80 mD
Heightabovefreewaterlev
el(m)
400
300
200
100
00 20 40
Sw(%)60 80 100
Chalk, 0.42, 4 mD
0 20 40Sw(%)
60 80 100
Micrite, 0.10, 0.1 mD
0 20 40Sw(%)
60 80 100
OilGas
OilGas
OilGas
OilGas
OilGas
OilGas
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108 Chapter 1-1 Calculation of Fluid Volumes In Situ (Accumulations): Static Properties
a long period of time), or by measuring the pressure gradient in oil through mini-tests carried
out at various depths (repetitive tests). Conducted according to professional standards bothmethods are expensive and consequently, when discussing real field cases, data uncertainty
must always be taken into account.
Fluctuations due to petrophysical variations (fixed FWL)
General case
Imagine a large limestone reservoir changing, due to sedimentological evolution, from porous
bioclastic grainstones to increasingly compact micritic formations exhibiting the petrophysical
characteristics described on Figure 1-1.52. While the free water level (FWL) remains
horizontal and stable throughout the structure, the original oil/water contact (OOWC) follows
the value equivalent to the access pressure. In the assumption of Figure 1-1.52, the altitude of
the water level increases from left (bioclastic grainstone) to right (compact micrite). To plot
the curves shown on Figure 1-1.52 we adopted the standard oil characteristics used in the
previous paragraph. The values are therefore representative. We observe that for the second
saturation profile (pelletoidal grainstone) which still corresponds to a reservoir rock, there is
already a shift of some ten metres. For the third and fourth profiles, the shifts reach several tens
of metres.
Obviously, the example shown on Figure1-1.52 is highly diagrammatic. It is based
mainly on an assumption of vertical homogeneousness. To return to a more realistic
situation, we would have to introduce vertical variability in order to show superimposed
water levels. This example nevertheless clearly shows that the notion of a flat and horizontalwater level, so frequently encountered in permeable reservoirs, is completely meaningless as
soon as we are faced with poorly permeable reservoirs, of micrite type for example.
Whenever we observe a fluctuation in water level, we must first consider the assumption
of a petrophysical variation.
Figure 1-1.52 Diagram of irregular hydrocarbon/water contactrelated to the lateral variation of the reservoir
1 2 3 4 5
0.33 0.23 0.22 0.15 0.10
K (mD) 300 7 1 03 0.01
HeightaboveF.W.L.(m)
Free WaterLevel
250
200
150
100
50
Oil Water
Contact
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1-1.2 Capillary Pressure in Case of Perfect Wettability 109
Case of fractured reservoirs
The saturation profiles 3 and 4 shown on Figure 1-1.52 correspond to poorly permeablereservoirs which will only yield good production if a network of open fractures creates high-
permeability drains. These matrices, poorly permeable but still exhibiting high porosity, and
therefore very oil-rich in the zones above the water level, can supply the network of
fractures. Some of the most productive oil fields in the world operate according to this
scheme.
One important feature of open fracture networks must be pointed out. These fractures
exhibit conducting apertures up to several hundred microns thick. As a result, they are no
longer subject to capillarity and the oil/water contact corresponds to the free water level. We
therefore observe in these reservoirs two different oil/water contacts, sometimes several tens
of metres apart, corresponding to the two media of highly contrasted petrophysical
properties, which coexist in these reservoirs (Fig.1-1.53). Since the open fractured medium
represents only a minute fraction of the total porous medium, the oil it contains is impossible
to detect using log analysis. Occasionally, some water saturated reservoir zones (matrix)
yield excellent oil production if an open fracture intersects the well. However, this
production only lasts as long as the open fracture network is supplied with oil but this is
outside the scope of our subject!
Figure 1-1.53 Position of the oil/water contact in fractured reservoirs
250
200
150
100
50
0
1Water Saturation
MATRIX OWC
FWL and FRACTURE OWC
HeightaboveF.W.Lorcapillarypressure
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110 Chapter 1-1 Calculation of Fluid Volumes In Situ (Accumulations): Static Properties
Extreme case of fluctuation of petrophysical origin: the stratigraphic trap
If we look at the fifth saturation profile on Figure 1-1.52, the access pressure of this veryfine micrite corresponds to a height of more than 200 m above free water level. If the
reservoir closure is less than this high value, the rock is totally water saturated and acts as a
cap rock. If we imagine that the type 5 rock corresponds to a lateral facies variation
upwards, in a monoclinal structure, we obtain a perfect example of stratigraphic trap. The
stratigraphic trap corresponds to the extreme stage of petrophysical fluctuation of the water
level.
We mentioned that this rock would act as capillary barrier (and therefore as cap rock) as
long as the closure is not high enough to induce a capillary pressure greater than the access
pressure. If the capillary pressure increases up to this threshold, then the barrier layer is
invaded by oil and, at least theoretically, the oil previously trapped can escape across the
ex-barrier and continue its secondary migration. We would therefore observe a geological
equivalent of the penetration by the non-wetting fluid through the semi-permeablemembrane in a restored state experiment ( 1-1.2.4, p. 73).
Unlike the case of shaly cap rock, the notion of cap rock in stratigraphic trap is often
related to the height of the oil column in the zone concerned. In shaly cap rocks, the access
pressure is often more than one hundred bars (which corresponds to a 5 km oil column,
according to our calculation assumption) and we may speak of absolute capillary barrier.
Fluctuations related to pressure variations
In the previous paragraph, we considered the case of a stable hydrostatic state and variable
petrophysical properties. We will now investigate an opposite situation in which a pressure
variation leads to a variation in OOWC (in a homogeneous petrophysical reservoir).
Pressure variations are induced by two main causes.
Pressure variations related to hydrodynamismThe logic we outlined above is based on the rules of hydrostatics, i.e. it assumes pressure
equilibrium, especially in the aquifer which acts as implicit reference. If the aquifer is active,
in other words if there is a pressure gradient in the horizontal plane causing a flow, the free
water level will be inclined in the same direction as the aquifer isobar lines. It will be tilted
in the direction of flow (Fig. 1-1.54). This pressure variation is easy to calculate for a given
aquifer flow. We will express this flow as filtration velocity (U). Remember ( 1-2.1.1,
p. 125) that the filtration velocity does not correspond to the displacement velocity of the
water particles but to the total quantity of water which crossed a plane normal to the flow
during the chosen reference period. The corresponding hydraulic gradient (in bar/cm) is
equal to this velocity in cm/s divided by the permeability in darcy (definition of the darcy).
To use more practical units, we will say that a filtration velocity of 1 m/year
corresponds to a gradient of about 300 millibar/km in a rock of permeability 1 D. In large
captive water tables of high permeability, the filtration velocity is less than 1 m/year (Table
1-2.1, p. 126). We may therefore consider that this value is an upper limit of the situation
found at shallow depths in terms of petroleum criteria.
The difference in depth (h) of the free water level induced by this hydrodynamic
pressure variation (P) is given by the hydrostatic formula: h = P/. This value can be
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1-1.2 Capillary Pressure in Case of Perfect Wettability 111
checked graphically on diagram 1-1.54 where P is clearly the capillary pressure at height
h on the vertical B. In the extreme case of a filtration velocity of 1 m/year, the difference
on the free water level value is therefore about 15 m/km, which corresponds to a very high
gradient on the oil/water contact.
However, the filtration velocity values corresponding to the reservoir aquifers are much
smaller. In a conventional oil field, therefore, the difference in water level related to
reasonable hydrodynamism will be much less than 1 m per kilometre.
Hydrodynamism comes back from time to time as a possible explanation for water leveltilting. In our opinion this is often unjustified. The hydrodynamic explanation of tilt in
the water level must be limited to very shallow reservoirs located on aquifers proven to be
highly active. At the very least, we must avoid the absurdity of using hydrodynamism to
explain a tilt associated with an aquifer with such little activity that water would have to
be injected to maintain production.
Figure 1-1.54 Hydrocarbon/water contact inclined due to hydrodynamism
Water A
Water B
Oil
h
P
BA
h
P
OOWC
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112 Chapter 1-1 Calculation of Fluid Volumes In Situ (Accumulations): Static Properties
Pressure variations related to modifications of the fluid types
We have seen that the main cause of the pressure difference between water and oil was thedifference in their densities (Pc =h). If a given reservoir is spread out geographically,
however, density variations may be caused by a number of factors. These factors include
(non exhaustive list several factors may be found in the same reservoir):
variation in oil type or gas content;
variation in water salinity;
variation in temperature under the effect of a geothermal variation.
Calculating the effect of these variations on the free water level and on the oil/water
contact is more difficult than in the previous case since assumptions must be made, on a case
by case basis, regarding the location of the pressure constants chosen as reference.
To give an example, Stenger [1999] used a temperature/salinity variation to explain a tilt
of about 0.5 m/km in the FWL on the Ghawar field (Saudi Arabia). Note that this variation is
only important since it extends over several hundred kilometres in this field, the largest inthe world.
b) Anhydrous production in zones of high water saturation
In conventional permeable reservoirs, anhydrous oil production zones are generally
associated with zones of lower water saturation This corresponds to the fact that the zones of
high saturation can only be transition zones in which the water is movable. This rule does
not apply in some reservoirs.
The extreme example of this problem was discussed when we mentioned earlier the case
of fractured reservoirs producing under the water level corresponding to the matrix.
This phenomenon may be observed in a more subtle way, at matrix scale, in limestone
reservoirs exhibiting highly contrasted double porosity (micro/macro seeGlossary Index).
Figure 1-1.55 shows the epoxy pore cast ( 2-2.1, p. 331) of an oolitic limestone exhibiting
both significant intraoolitic microporosity, contributing in particular to the high porosity
(0.34), and a well-developed intergranular macroporosity, inducing very high permeability
(600 mD). The porosimetry curve, converted into saturation profile for a standard water/oil
pair, indicates that at 25 m above free water level, the water saturation is about 0.5 (and 0.40
at 75 m). This high water saturation corresponds to almost non-movable water in the
microporosity and the rock may yield abundant anhydrous production. This observation is
particularly important for zones of low hydrocarbon column.
This represents a further example of the petrophysical features associated with the
double matrix media encountered so frequently in carbonate rocks. This is why, during
exploration phases, it is often recommended to carry out a systematic test of the porous
limestone layers, irrespective of the saturation data obtained by log analysis.
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144 Chapter 1-2 Fluid Recovery and Modelling: Dynamic Properties
1-2.1.4 Porosity/Permeability relations in rocks
The porosity/permeability relations in rocks are extremely useful in practice, mainly since
permeability is a no-logging parameter: despite all attempts (and the corresponding
publications), there is no reliable log analysis method to continuously measure the
permeability of the reservoir rocks in the borehole.
Discrete hydraulic methods are obviously available (e.g. mini-test), but they are costly.
Reservoir geologists therefore would like to find a relation between porosity (easily
measured using log analysis techniques) and permeability, so that it can be easily deduced.
Most of the time, this is a risky operation.
The complexity of the -Krelation is related to the complexity of the porous space itself.
We will therefore start by describing the simple case of the ideal intergranular porous
medium as encountered in the Fontainebleau sandstones. We will then study the carbonate
rocks and the common sandstones.
A) Simple porous networks: Example of Fontainebleau Sandstone
a) Fontainebleau sandstones (Fig. 1-2.13)
The Fontainebleau sandstones (Paris region, France) are a rare example of simple natural
porous media (intergranular porosity) exhibiting large porosity variations (from about 0.02
to 0.28) with no major change of grain granulometry. This is an ideal example on which to
study the porosity/permeability relation.
Fontainebleau sandstone consists mainly of quartz grains subjected to a long period of
erosion and good granulometry sorting before being deposited during the Stampian age, in
coastal dunes. The original deposit consists of quartz sands with subspherical
monocrystalline grains of diameter in the region of 250 m [Jacquin 1964, in French]. Thesedunes underwent a complex and still poorly understood geochemical evolution leading,
firstly, to the total dissolution of bioclastic limestone fragments probably abundant
originally and, secondly, to a more or less pronounced siliceous cementation. Silica was
deposited between the grains, as quartz in crystalline continuity with them (syntactic
cement). This syntactic cementation explains the holomorphous crystal shape frequently
taken by the grains. It also explains why the pore walls sometimes correspond to almost
perfect crystalline planes (bottom photograph on Figure 1-2.13). The composition of
Fontainebleau sandstones is therefore exceptionally simple: 99.8% silica (mainly quartz
crystals).
It may be surprising to note that the variable cementation does not result in a significant
variation in the apparent grain diameter. This is due to the fact that cementation occurs by
progressive plugging of the intergranular space.
The exceptional simplicity of the solid phase matches the simplicity of the porous phase:
it is exclusively intergranular. The microcracks at the grain contacts, observed in some cases
studied below (Fig. 1-2.16), must be considered separately. Although negligible in terms of
volume (porosity), these microcracks may have major consequences on the acoustic
properties or on the permeability in the range of very low porosities.
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1-2.1 Intrinsic Permeability 145
b) ThefKrelation
Numerous studies have been conducted on the porosity/permeability relation. A first
publication [Jacquin, 1964, in French], concerns a small number of samples (about 60) but
includes accurate measurements of grain dimensions in thin section, thereby allowing
normalisation by the parameter K/d2. A study on 240 samples of diameter 40 mm and length
Figure 1-2.13 Epoxy pore cast of Fontainebleau sandstone,Observation under scanning electron microscope, stereographic representation.
The mean porosities of the samples (from top to bottom) are: 0.28, 0.21 and 0.05. [Bourbi et al., 1987]
500 m
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146 Chapter 1-2 Fluid Recovery and Modelling: Dynamic Properties
between 40 mm and 80 mm [Bourbi and Zinszner, 1985] indicates a double trend for the
K relation. For high porosities (between 0.08 and 0.25), all the experimental points liefairly well on a curve of type K = f(3). Note that the power 3 corresponds to that of the
Carman-Kozeny equation. For low porosities (< 0.08), we may observe large exponents
suggesting a percolation threshold ( 1-2.1.3D).
Example of the Milly la Fort normal sandstones
In this book, we give results of a much larger sampling (but of the same type as the 1985
samples and including them). To simplify the analysis, it is best to identify the origins of the
various groups of samples studied. The results shown on Figure 1-2.14 concern about 340
samples from a very restricted geographical area (Milly la Fort). Due to their geological
unity, the quality of the porosity/permeability relation is quite exceptional. The
subdivisions (MZ2, etc.) correspond to different blocks measuring several decimetres in
size, obtained from various points in a limited number of quarries. Note that the
permeabilities of block MZ10 are slightly above the average: the granulometry is probablyslightly coarser.
Air permeability values are measured in room condition (falling head permeameter,
1-2.1.2A, p. 131). The experimental permeabilities below 100 mD have been corrected for
the Klinkenberg effect according to the semiempirical formula ( 1-2.1.2A)
On Figures 1-2.14 the permeability axis uses a logarithmic scale (corresponding to the
log-normal distribution of permeabilities). We describe both types of axis used for porosity.
On the left hand figure, we use a linear axis (normal distribution of porosities) and on the
right hand figure a logarithmic axis to show the power laws.
In semi-logarithmic representation, which is generally used for reservoir
characterisation, note the exceptional quality of this -Krelation. To our knowledge, this is
the only example of its type.
In logarithmic representation, we can see the slopes of the power laws: for the poroussamples (> 0.09), a slope of about 3.25 gives a fairly good picture of the K= f(n) relation.
Figure 1-2.14 Porosity-Permeability relation in the Milly la Fort normal Fontainebleau sandstones.The porosities are presented in the two usual ways: linear scale (semi-log graph on the left)
and logarithmic scale (on the right). The subdivisions (MZ2, etc.) correspond to different blocks
0.1
0.010.01 0.02 0.03
Porosity (fractional)Porosity (fractional)
Permeability(mD)
Permeability(mD)
0.1
1
10
100
1 000
10 000
slope 3.25
slope 10
0.1
1
10
100
1 000
10 000
MZ2
MZ3
MZ4
MZ7
MZ10
MZ15
MZ16
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1-2.1 Intrinsic Permeability 147
The value of the exponent is similar to that observed in the earlier studies. For low porosity
samples (0.04 to 0.06), the Klinkenberg correction increases the value of this exponent evenmore, reaching 10. Such high exponents can only be explained by a percolation threshold
(about 0.05 porosity).
To profit from the exceptional quality of the results on the Milly la Fort sampling, we
calculate the polynomial regression best fitting the experimental values, in order to obtain a
basic datum for estimation of the -Klaws of intergranular porosity media.
A polynomial regression of order 3, on logarithmic values of and K, of type
logK= a(log )3 + b(log)2 + c(log)+ d,
with the above values (corresponding to the case of porosities expressed as percentages)gives excellent results for porosities between 4% and 25%.
Microcrack facies
Some poorly porous samples have microcracks. They consist of strongly pronounced
grain joints that can be observed on thin section but even more clearly on epoxy pore cast
(Figure 1-2.16). These microcrack facies have been identified due to the very strong
acoustic anomalies generated by these cracks [Bourbi and Zinszner, 1985]. These facies
must be considered separately when studying the -Krelation. Figure 1-2.15 shows some
sixty values corresponding to this type of sample (4 different series). As previously, the
semiempirical Klinkenberg correction was carried out on the permeability values. By
comparison, the values for the Milly samples are expressed as a sliding geometric mean (for
clarity purposes).
Note that the permeabilities of the microcracked samples are significantly larger than
the Milly samples of equivalent porosity. This seems normal since the crack porosity
becomes more efficient in terms of permeability than the intergranular porosity. Note also
a b c d
11.17 40.29 51.6 20.22
Figure 1-2.15 Porosity-Permeability relation in microcrack Fontainebleau sandstones.The standard values correspond to the sliding geometric means of Milly samples
0.01 0.1
Porosity (fractional)
Permeability(mD)
0.01
0.1
1
10
100
1 000
IN6
M52
MA81
MA82
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148 Chapter 1-2 Fluid Recovery and Modelling: Dynamic Properties
that, for very poorly porous samples (< 0.04), the drop in permeability is less significant
than might have been expected by extrapolating the Milly results: the percolation threshold
effect is less marked, once again due to the special properties of crack porosity.
This shows that, even in what seems to be the simplest case, adding a secondphenomenon may significantly disturb the analysis. The microcrack facies must be
identified and isolated in order to restore the simplicity of the Fontainebleau sandstone
-Klaw and to demonstrate the unquestionable percolation threshold at about 0.05 porosity.
Lastly, note that this microcrack porosity is extremely sensitive to the effect of
differential pressure (see 1-2.1.5, p. 164 and 2-1.1.2, p. 267). It is highly likely that
application of the moderate differential pressure would be sufficient to close these
microcracks and therefore eliminate their petrophysical effect. This is quite spectacular
concerning elastic wave propagation ( 1-3.2.4, p. 233). No data are available on the
permeability of Fontainebleau sandstones with microcrack facies measured under
pressure, but it is highly likely that application of a differential pressure would remove this
microcrack effect.
c) Conclusion
Fontainebleau sandstones represent an ideal example on which to study the -Krelation.
They can be used to determine a practical standard for the intergranular porous space of
isogranular packings. The polynomial regression on Milly values (mean grain diameter
d = 250 m) could be extended to different granulometries by using the K/d2normalisation.
Figure 1-2.16 Fontainebleau sandstone with microcrack facies ( = 0.06). Photograph of thin section(red epoxy injected, 2-2.1.1, p. 325) on the left and of epoxy pore cast, on the right ( 2-2.1.3, p. 331).
Microcracks, which correspond to grain contacts, can be clearly seen on the epoxy pore cast
500 m
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1-2.1 Intrinsic Permeability 149
The percolation threshold at about 0.05 porosity is also clearly determined; it will prove
extremely useful when discussing -Krelations in double-porosity limestones.
B) Porosity/Permeability relations in carbonate rocks
The situation with carbonates is strikingly different from that observed in Fontainebleau
sandstones. Figure 1-2.17 shows the -Krelation (air permeability) for a set of about 1 500
limestones and dolomites samples (diameter 4 cm) corresponding to a large variety of
petrogaphic texture. Note that in line with standard practice, and in spite of the fact that it is
poorly adapted to the power laws, we have adopted the semilogarithmic representation
which makes the graphs much easier to read on the porosity axis. The permeability
dispersion is very high since, on the porosity interval most frequently encountered in
reservoir rocks (0.1 to 0.3), the values extend over nearly four orders of magnitude. Put so
bluntly, it is clear that there is no -Krelation! Considering the microtexture of the rocks,
some general trends may nevertheless be observed.
a) Dolomites
On Figures 1-2.17, the points corresponding to dolomites and dolomitic limestones are
separated from the limestones. The dolomite/dolomitic limestone/limestone separation was
made using the criterion of matrix density ( 1-1.1.5, p. 26) choosing 2 770 kg/m3as the
lower limit of the dolomite and 2 710 kg/m3as the upper limit of the limestones. We will
only consider the case of the dolomites. Far fewer points are available (about 50) than for the
limestones. We can nevertheless make a few important comments. Although dolomites are
present throughout the -Kspace (Fig.1-2.17), they are mostly represented in the region of
high permeabilities. The reason is quite simple: there is no microporosity in true dolomites
whereas it plays a major role in limestones (this point will be strongly emphasised in the
next paragraph).
Sucrosic dolomite, vuggy dolomite
Two main contrasting features can be observed in dolomites.
The dolomite has a granular structure (sucrosic dolomite) and, in the -Kspace, these
dolomites are similar to sandstones due to absence of microporosity.
The dolomite has a vuggy structure, in which case the porosity is concentrated in
sometimes very poorly interconnected vugs and permeability is relatively low.
Dolomitic drains, Super-K
We can see on Figure 1-2.17 that the sample with the highest permeability (0.3, 70 D) is a
dolomite. This sample comes from a dolomitised zone inside an oolitic barrier (France, core
sample).
This type of dolomite is interesting due to the central role it plays in some petroleum
reservoirs by creating drains which are thin (less than 1 m) but which exhibit very high
permeability (up to 100 D). Some excellent examples of these super-Ks can be found in
the Ghawar field (Saudi Arabia). A detailed description is given in Meyer et al.[2000]. A
simplified example of these super-Ks is illustrated on Figure 1-2.18. It corresponds to the
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150 Chapter 1-2 Fluid Recovery and Modelling: Dynamic Properties
case of a very good producing well (over 10 000 barrels per day). The production log
analysis (flowmeter: FLT1) shows that most of the production comes from a single very thin
layer. At this layer, the drilling hole diameter, as shown by the caliper (CAL1), is larger than
the nominal value (caving in a highly brittle rock) and the porosity log analyses (NPLE and
RHOBE) are disturbed by this caving phenomenon. We may consider, however, that thelayer porosity is very high (0.30 or more).
This reservoir has been cored and recovery is almost perfect (more than 95%) but the
super-K cannot be observed on the core porosity-permeability log (Log(Kh) and CORE-
PORE). The highly brittle rock forming the super Kwas flushed away during the coring
operation. This is an example of the principle according to which, even during an excellent
coring operation, some extremely important details of the reservoir may be overlooked.
Figure 1-2.19 shows photographs of thin sections from the French example discussed
above (the samples do not belong to the same database as that used for Figure 1-2.17 and are
therefore not represented). The samples were prepared using several resins ( 2-2.2.2,
p. 336), but to understand the -Krelation, the undifferentiated total porosity (blue, yellow,
red) is sufficient. Both samples are totally dolomitised (ma> 2 800 kg/m3) and the oolites
clearly visible on the photographs are only ghosts. Photograph a) (= 0.18; K= 4 D)shows a very vuggy system which is highly connected and responsible for the high
permeability. The sample of photographb)( = 0.06; K= 0.1 mD), although located at a
depth of less than 50 cm below sample a, corresponds to a totally different facies. It has only
very poorly connected vugs, hence the very low permeability. On photograph b, we can see
extensive white areas corresponding to large dolomite crystals. These large crystals take the
Figure 1-2.17 Porosity-Permeability relation in carbonate rocks(air permeability, Klinkenberg effect not corrected, about 1500 samples of diameter 4 cm)
0.010.1 0.2
Porosity (%)
Permeability(mD)
0.3 0.4 0.50
0.1
1
10
100
1 000
10 000
100 000
Limestone
Dolomitic Lmst
Dolomite
Fontainebleau
Power 3Power 5
Power 7
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1-2.1 Intrinsic Permeability 151
geometrical positions of the extensive red areas on photograph a. They are the result of
cementation after the vacuolarisation phase of photograph a. This recrystallisation has been
extremely erratic, which explains the petrophysical variations between samples located
several tens of centimetres apart in the geological series.
b) Limestones
The values reproduced on Figure 1-2.20 correspond to some 650 samples from the database
of Figure 1-2.17, for which a limited amount of information concerning the microstructure is
available.
Figure 1-2.18 Example of well log analysis in a Super-K dolomitic reservoir
GRE: -ray in API unit; CAL1 (grey curve) caliper graduated in inches.
NPLE (continuous curve): Neutron porosity (fractional porosity) ROBE (dashes): bulk density.
FLT1: flowmeter (as a percentage of the total production).
Log(KH): air permeability on plugs with horizontal axis (logarithmic scale in mD).
CORE-PORE: Porosity on the same core samples (scale in percentage), the neutron porosity curve is dupli-
cated for comparison (excellent agreement).
100
m
Courtesy Saudi Aramco
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152 Chapter 1-2 Fluid Recovery and Modelling: Dynamic Properties
Figure 1-2.19 Photographs of thin sections of samples from a dolomitised zone inside an oolitic barrier(France, core sample). The samples were prepared using 3 resins ( 2-2.2.2, p. 336).
Pores of access radius less than 0.3 m are shown in blue. The red areas correspond to porosity displaceableby spontaneous imbibition, the yellow areas to trapped porosity
Photoa)(top): = 0.18;K= 4 D.
Photo b)(bottom): = 0.06; K= 0.1mD, note that all the vugs correspond to trapped porosity.
5 mm
a
b
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154 Chapter 1-2 Fluid Recovery and Modelling: Dynamic Properties
Figure 1-2.21 Porosity-Permeability relation in oolitic limestones (values extracted from Figure 1-2.17).Epoxy pore casts ( 2-2.1.3, p. 330) photographed using scanning electron microscope (SEM).
Same scale for all six photographs
Limestonesa, b, d: core samples.
Limestonec: oolite miliaire outcrop, Normandy (France).
Limestonee: outcrop, Chaumont (France); Limestonef: outcrop, Brauvilliers (France).
a b c
d
f
1 mm
0.01
0.1
1
10
100
1 000
10 000
Porosity (%)
Permeability(mD)
Oolite
Fontainebleau
Power 3
Power 5
Power 7
e
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
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1-2.1 Intrinsic Permeability 155
Micrites
Micrites (Fig. 1-2.22) are rocks mainly formed from microcrystalline calcite. The -Krelation, however, is quite different from those of the oolitic limestones. In the -Kspace,
the micrites are grouped along a line corresponding approximately to a power 3 law going
through = 0.1; K = 0.1 mD. This relative simplicity of the -K relation in micrites is
explained by the fact that they only have a single type of porosity. The porosimetry spectra
(Fig. 1-2.23) are clearly unimodal and contrast with the other limestones.
Main trends and limiting values of f-Krelations in limestone rocks
So far, we have emphasised the extreme diversity of -Krelations. However we can make a
few observations which will prove useful when studying limestone reservoirs:
Figure 1-2.22 Micritic limestones (Mudstone) photographed using SEM. On the left, photograph of naturalrock (fracture); on the right, epoxy pore cast
a) Core sample (Middle East); = 0.29; K= 1.5 mD.
b) White Chalk (outcrop) from the Paris Basin; = 0.44; K= 6 mD.
10 m
a
b
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156 Chapter 1-2 Fluid Recovery and Modelling: Dynamic Properties
Limits of the -Kspace.
The various -Krelations described in this section respect the matrix value criterion( 2-1.3, p. 311). They come from plugs and the minimum homogenisation volume is
millimetric. We can see on Figure 1-2.20 that these values define a -Kspace whose
limits are quite well defined
By the Fontainebleau sandstone line towards the high permeabilities
By the mudstone line (power 3 law) towards the low permeabilities
Although these limits are very broad, they are nevertheless practical. When studying
reservoirs, special attention must be paid to values outside this area. They generally
indicate measurement errors or faulty samples (e.g. fissured plug). In the other cases,
however, a special study could prove well worthwhile.
Main trends
Some main trends in the -K relation may also be observed according to the
petrographic texture of the limestones (Fig. 1-2.20).
The very poorly permeable limestones (K < 0.1 mD) have not been shown onFigure 1-2.20. The porosity of limestones whose permeability is greater than this
low value is generally more than 10%, apart from the important exception of crinoi-
dal limestones which have very little microporosity, hence the high permeabilities.
Some oolitic grainstones lie within the same area of the-Kspace, for the same rea-
son: proportionally very low microporosity.
For the other types of limestone, we observe a point of convergence at about
= 0.1; K= 0.1 mD. If power 3, 5, 7 law graphs are plotted from this point, we
observe that the mudstones are grouped on the power 3 law (see above), the
wackestone-pelstones around the power 5 line and the bioclastic grain-packstones
around the power 7 line. Although these are obviously very general observations
(except for the mudstones), they may prove useful when looking for orders of mag-
nitude, during modelling for example.
c) Conclusion on thef-Krelations in carbonates
We have described the vast diversity of -Krelations in limestones and have returned on
several occasions to the unique cause of this diversity (and of this absence of -Krelation in
the strict sense). In limestone rocks (apart from mudstones), at least two types of porosity
affect the petrophysical characteristics, in quite different ways.
The microporosity (microconnected porosity) always present in the allochems and
matrix (mud).
The macroconnected porosity sometimes found between the allochems (intergranu-
lar), and also rarely in the dissolution vugs if they are present in sufficient num-
bers to be interconnected.
Only macroconnected porosity plays a significant role in permeability. We would
therefore need to plot the macroconnectedvs.Krelations to obtain a rough estimation. This
approach would, however, be both costly in terms of porosimetric measurement and of little
practical application, since the -K relations are of most use when there are no samples
(drilling).
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1-2.1 Intrinsic Permeability 157
The porosimetric diversity of carb
top related